Magnetic-field-driven director configuration transitions in radial nematic liquid crystal droplets.

We study the director configurations of nematic liquid crystal (NLC) droplets with homeotropic anchoring in a magnetic field and report observation of a magnetic-field-driven transition from a deformed radial to an axial-with-defect configuration. Magnetic-field-induced transitions in NLC droplets differ fundamentally from the traditional planar Freedericksz transition due to the spherical droplet geometry and resulting topological defect. This transition has been studied theoretically, but the director configurations and mechanism of defect evolution in an applied magnetic field have yet to be observed experimentally. To this end, we combine polarized optical microscopy with a variable electromagnet (≤1 T) for continuous observation of droplet director fields, and we employ Landau-de Gennes numerical simulations to elucidate the director configurations and first-order nature of the transition. We report a configuration transition from point defect to ring defect at a critical field, which varies inversely with droplet radius and is relatively independent of surfactant type and concentration. We also estimate anchoring strengths of commonly used surfactants at the NLC-aqueous interface.

Giant director fluctuations in liquid crystal drops.

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central "hedgehog" defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius R_{2}, containing a spherical central core of radius R_{1} and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value µ_{c} of the ratio µ=R_{2}/R_{1}. When µ<µ_{c}, the mode has positive energy, indicating that the radial hedgehog state is stable; when µ>µ_{c}, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for µ near µ_{c}. A collapse of the experimental data corroborates model predictions for µ<µ_{c} and provides an estimate of the defect core size.

Theory of director fluctuations about a hedgehog defect in a nematic drop.

We present calculations of eigenmode energies and wave functions of both azimuthal and polar distortions of the nematic director relative to a radial hedgehog trapped in a spherical drop with a smaller concentric spherical droplet at its core. All surfaces interior to the drop have perpendicular (homeotropic) boundary conditions. We also calculate director correlation functions and their relaxation times. Of particular interest is a critical mode whose energy, with fixed Frank constants, vanishes as the ratio µ=R_{2}/R_{1} increases toward a critical value µ_{c}, where R_{2} is the radius of the drop and R_{1} that of the inner droplet, and then becomes negative for µ>µ_{c}. Our calculations form a basis for interpreting experimental measurements of director fluctuations relative to a radial hedgehog state in a spherical drop. We compare results with those obtained by previous investigations, which use a calculational approach different from ours, and with our experimental observations.

Rods in a lyotropic chromonic liquid crystal: emergence of chirality, symmetry-breaking alignment, and caged angular diffusion.

In lyotropic chromonic liquid crystals (LCLCs), twist distortion of the nematic director costs much less energy than splay or bend distortion. This feature leads to novel mirror-symmetry breaking director configurations when the LCLCs are confined by interfaces or contain suspended particles. Spherical colloids in an aligned LCLC nematic phase, for example, induce chiral director perturbations ("twisted tails"). The asymmetry of rod-like particles in an aligned LCLC offer a richer set of possibilities due to their aspect ratio (α) and mean orientation angle (〈θ〉) between their long axis and the uniform far-field director. Here we report on the director configuration, equilibrium orientation, and angular diffusion of rod-like particles with planar anchoring suspended in an aligned LCLC. Video microscopy reveals, counterintuitively, that two-thirds of the rods have an angled equilibrium orientation (〈θ〉 ≠ 0) that decreases with increasing α, while only one-third of the rods are aligned (〈θ〉 = 0). Polarized optical video-microscopy and Landau-de Gennes numerical modeling demonstrate that the angled and aligned rods are accompanied by distinct chiral director configurations. Angled rods have a longitudinal mirror plane (LMP) parallel to their long axis and approximately parallel to the substrate walls. Aligned rods have a transverse and longitudinal mirror plane (TLMP), where the transverse mirror plane is perpendicular to the rod's long axis. Effectively, the small twist elastic constant of LCLCs promotes chiral director configurations that modify the natural tendency of rods to orient along the far-field director. Additional diffusion experiments confirm that rods are angularly confined with strength that depends on α.

Author Correction: Molecular heterogeneity drives reconfigurable nematic liquid crystal drops.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Molecular heterogeneity drives reconfigurable nematic liquid crystal drops.

With few exceptions1-3, polydispersity or molecular heterogeneity in matter tends to impede self-assembly and state transformation. For example, shape transformations of liquid droplets with monodisperse ingredients have been reported in equilibrium4-7 and non-equilibrium studies8,9, and these transition phenomena were understood on the basis of homogeneous material responses. Here, by contrast, we study equilibrium suspensions of drops composed of polydisperse nematic liquid crystal oligomers (NLCOs). Surprisingly, molecular heterogeneity in the polydisperse drops promotes reversible shape transitions to a rich variety of non-spherical morphologies with unique internal structure. We find that variation of oligomer chain length distribution, temperature, and surfactant concentration alters the balance between NLCO elastic energy and interfacial energy, and drives formation of nematic structures that range from roughened spheres to 'flower' shapes to branched filamentous networks with controllable diameters. The branched structures with confined liquid crystal director fields can be produced reversibly over areas of at least one square centimetre and can be converted into liquid crystal elastomers by ultraviolet curing. Observations and modelling reveal that chain length polydispersity plays a crucial role in driving these morphogenic phenomena, via spatial segregation. This insight suggests new routes for encoding network structure and function in soft materials.